Autonomy, a British software company, once seemed to Hewlett-Packard to be a good purchase candidate. Western investors were once eager to buy into Chinese companies that had secured listings on U.S. exchanges.

Neither idea seems so hot now, however, and both these changes in sentiment raise awkward questions for the "Big Four" accounting firms, Deloitte, Ernst & Young, PwC and KPMG.

Hewlett-Packard came first: The computer giant announced last month that it was writing down the value of Autonomy by $8.8 billion, in part because of "accounting improprieties, misrepresentations and disclosure failures."

Mike Lynch, Autonomy's former boss, denies the charges and has set up a website demanding that HP detail its accusations.

With so few global auditors to choose from, a saga like this ends up ensnaring all of them. Deloitte was Autonomy's auditor, and Ernst & Young is Hewlett-Packard's. KPMG provided advice on the deal, and PwC has been hired by HP to sort through the mess.

If HP's claims are true, Deloitte -- as Autonomy's auditor -- will be the one in the cross hairs. If they are false, Ernst & Young, which signed off on HP's huge write-down of Autonomy, will have a great deal of explaining to do. HP says that the third of the Big Four, KPMG, "audited" the deal, but KPMG says it provided only a "limited set of non-audit-related services."

Deloitte has most reason to be nervous. As well as auditing Autonomy, it provided $6.7 million in non-audit services over seven years, prompting critics to raise familiar questions about conflicts between accountants' auditing duties and their consulting work. Deloitte advised Autonomy on executive pay, for example, something forbidden under America's Sarbanes-Oxley law but is permitted in Britain.

Moreover, last year Deloitte Luxembourg announced a close partnership with Autonomy to roll out a piece of Autonomy software.

The HP-Autonomy saga points to another feature of the Big Four's business model: The quartet market themselves as seamless global firms, but in fact they are a string of legally independent local partnerships. That is why Britain's Deloitte LLP can do things that would be forbidden for Deloitte LLP in America, despite their common membership in the Deloitte Touche Tohmatsu network.

On Dec. 3 this network structure came under attack from another quarter. The U.S. Securities and Exchanges Commission charged the Big Four and a smaller firm, BDO, for refusing to share documents related to audits of troubled Chinese firms listed on American exchanges.

Chinese divisions of the Big Four have audited several Chinese firms that listed abroad and then tanked. Prominent among these are Longtop Financial, a technology firm that since has been delisted in America, and Sino Forest, which Canadian authorities are investigating for allegedly faking forestry assets.

American regulators, including the SEC and the Public Company Accounting Oversight Board, have been demanding the work papers for the controversial audits from the Chinese affiliates. That puts the auditors in a bind. American regulators must ensure that the foreign auditors of firms listed in America are doing their job properly, but Chinese laws forbid the sharing of those documents, on the grounds that vaguely defined "state secrets" might surface.

For a while, Sino-American negotiations seemed to be making some progress on a compromise. A few months ago officials from the oversight board were allowed to observe their Chinese counterparts during a "trust-building" exercise. A meeting between the two sides in November appears to have ended frostily, however, and the SEC hardened its position this month by declaring that "firms that conduct audits knowing that they cannot comply with laws requiring access to these work papers face serious sanctions."

The oversight board is expected to declare by year's end that, if a foreign auditor has not been inspected properly by American authorities, it will be deregistered.

If such a rule is upheld by courts and confirmed as policy, it would mean that the Big Four's affiliates in China could lose many multinationals as clients, because American laws require firms to use registered auditors. It might also force the exit of scores of Chinese firms from U.S. securities exchanges.

The Big Four claim that their global scale and multidisciplinary scope are good things. In one sense they are right: Consulting is the fastest-growing of the Big Four's businesses. However, the events of the past few weeks show that there are perils, too, in trying to have the best of all worlds.

The operator of a Kansas water park where a boy was killed on a giant waterslide in 2016 says the park won't open for the season until safety issues raised in a recent state audit are resolved, though it believes the audit stemmed from a "malicious effort" to "stir up unfounded fear."